ON INSTRUMENTS FROM ITAL Y. 101 



and in the distance the Tower of Pisa, from which, by letting fall 

 bodies of different substances, he first showed how, but for the resis- 

 tance of the medium through which they pass, they would all fall in the 

 same time. Partly, perhaps, on account of being badly requited, 

 Galileo left the University of Pisa, and in 1592 we find him mathe- 

 matical lecturer at the University of Padua. 



It was here that for the convenience of the youth whom he had to 

 instruct in the arts of fortification and mechanics, he invented his pro- 

 portional compass, also called military compass. This is one of the 

 many which he himself made. On one side may be seen four sets of 

 lines, they are : 



Arithmetical lines, which serve for the division of lines, the solution 

 of the Rule of Three, the equalization of money, the calculation of 

 interest. 



Geometrical lines, for reducing proportionally superficial figures, 

 extracting the square root, regulating the front and flank formations 

 of armies, and finding the mean proportional. 



Stereometrical lines, for the proportional reduction of similar solids, 

 the extraction of the cube root, the finding of two mean proportionals, 

 and for the transformation of a parallelepiped into a cube. 



Metallic lines, for finding the proportional weights of metals, and 

 other substances, for transforming a given body into one of another 

 material and of a given weight. 



On the other side of the instrument are : 



Poly graphic lines, for describing regular polygons, and dividing the 

 circumference into equal parts. 



Tetragonical lines, for squaring the circle or any other regular 

 figure, for reducing several regular figures to one figure, and for 

 transforming an irregular rectilineal figure into a regular one. 



Joined lines, used in the squaring of the various portions of the 

 circle and of other figures contained by parts of the circumference, or 

 by straight and curved lines together. 



There is joined to the compass, as you see, a quadrant, which, 

 besides the usual divisions of the astronomical compass, has engraved 

 on it a squadron of bombardiers, and in addition, these transversal 

 lines, used for taking the inclination of the scarp of a wall. 



From Galileo's own correspondence we gather that in 1598 he had 



